See also: Royal Karate
Anya is one of the three (two in the anime) meisters shown to use Tsugumi Harudori's weapon form throughout the series and she proves to be very efficient in combat as well as immensely skilled, despite being in the N.O.T Class and her upbringing. She is very competent in using a staff weapon, it being what seems to be her forte to the point she'll even use a baseball as a spear and shown to be incredibly powerful in doing so.
She also mentions that she was forced to learn Royal Karate back at her castle, making her a competent fighter. However, her inexperience in street fights lets her down at some points as she can get too nervous, and without a Weapon partner, she cannot fight as well. As such, she was no match for the Protoype 2 Traitor or even Akane☆Hoshi. Meme Tatane is possibly stronger than her in terms of physical combat. However it is still shown that she is pretty athletic and could fight pretty skillfull without a weapon which is shown when she fought a undercontrol Meme with her stinger.
In addition, she has the ability to analytically read individuals well. She was able to correctly analyze that Tsugumi changed her hairstyle to copy someone else and later called out Soul on being fake, which was correct due to Soul's yearning to be away from his family.
Due to her inexperience in real fights, she's often gets nervous and tends to be her undoing. Because of this, she has lost to those such as the Traitor(Prototype 2) and the Demon Twin Guns, Liz and Patty.